Systemic risk and crisis management:
A CoVaR approach ✩Katsutoshi Shimizua,∗a Department of Economics, Nagoya University

Abstract
This paper examines the eﬀects of a regulator’s crisis management on systemic risk
as measured by the delta conditional value-at-risk (CoVaR) during the financial crisis
in Japan. We evaluate the various management measures primarily in terms of theirliquidity provision/capital infusion eﬀects as well as adverse contagion eﬀects. The
findings of the study generally support evidence for the liquidity provision/capital infusion eﬀect, but favor the adverse contagion eﬀect for public fund injection programswith multiple recipients. In addition, the management restrictions accompanying injection prrograms or the moral hazard with failure resolution might have aggravatedthe systemic risk. Furthermore, although we confirm that the average systemic riskof the largest banks is higher than that of other banks, we do not necessarily observe
the amplified eﬀects of the former on the latter. Lastly, crisis management does not
eﬀectively work for the systemic tail risk.

Keywords: Systemic risk, CoVaR, deposit insurance, prompt corrective action,
public fund injection, bank failure, liquidity, contagion, too-big-to-fail policy, tail risk
JEL classification: G21; G28; G18; G14; G32

March 20, 2015

✩ The author acknowledges funding support from Grant-in-Aid for Scientific Research.
∗ Corresponding author:

Katsutoshi Shimizu, Department of Economics, Nagoya Univer-sity.
Address: Furo-cho, Chikusa-ku, Nagoya, Aichi, 464-8601, Japan. Tel.: +81-52-789-2378,
Fax: +81-52-789-2378
Email address: shimizu@soec.nagoya-u.ac.jp (Katsutoshi Shimizu)

1. Introduction
During a financial crisis, we experience a successive sequence of bank failures. A large-scale breakdown of financial institutions has adverse eﬀects on
the financial markets and overall economy. A liquidity shortage in a system
of interconnected banks and a decline in asset prices through fire sales worsen
the stability of financial markets. The failure of one financial institution may
trigger the failure of another, leading to a surge in systemic risk. Even underfull coverage deposit insurance, failures seem to spill over to others. Regulators,
occasionally considered in the past, are now widely considered responsible formanaging crises in a manner that does not aggravate systemic risk. This paper
examines whether regulators’ crisis management had significantly amelioratingeﬀects on the spillover from a distressed bank to the financial markets.
Since the recent global financial crisis, academics and financial regulators
have been more highly concerned with the crisis management. However, empirical research on the eﬀects of crisis management on the systemic risk seems
under-researched. We broadly define the four types of crisis management: publicfund injection (abbreviated as PFI) programs; prompt corrective actions (PCA);
failure resolution scheme (FRS), such as purchase and assumption (P&A) agreement; and deposit insurance reforms (DIR) act that implement blanket guarantees in extreme cases. Our analyses focus on the systemic risk and management
measures during the Japanese financial crisis in the 1990s and early 2000s, because the prolonged and serious nature of the crisis provides an environment
rich in these management measures.
We examine the various hypotheses on the eﬀects of the four measures on
systemic risk. First, systemic risk surges because of liquidity shocks in the senseof the celebrated work of Diamond and Dybvig (1983). Liquidity provisions thatcan be used to pay depositors and to provide liquidity to distressed client bor-

1

rowers lower the probability of individual runs (Allen and Gale (2000)). In addition, preventing insolvency through capital infusions leads to lower systemic risk
(Freixas et al. (2000)). We call these mechanisms liquidity provision/capital infusion eﬀects. Furthermore, liquidity shocks spread through contagion, because
financial claims overlap across banks and/or borrowers. Because the interbank
links enables the losses of one bank to spread over to other banks, liquidity
provisions and/or preventing insolvency of one distressed bank by capital infusions may prevent the contagion of failures, leading to lower systemic risk
(Diamond and Rajan (2005) and two papers previously cited). We call thiseﬀect an adverse contagion eﬀect.
In PCA and the FRS, these two eﬀects may also be observed. PCA may prevent distressed banks from failing or may mitigate the damages to the financial
system through early appropriate orders. The rescue package in which the failedbank is sold to another healthy bank may also prevent contagious failures bysmoothly isolating banks at default from the market (Acharya and Yorulmazer(2008), Gorton and Huang (2004), Freixas et al. (2000)). In adiition, under theso-called blanket guarantee, no general creditors of the failed bank incur any
losses. Therefore, the blanket guarantee may ameliorate systemic risk in thesense that the insolvency of one bank does not lead to a liquidity shortage ofother banks, borrowers, and depositors.
Together with these two eﬀects, we consider the adverse eﬀects of crisis
management on systemic risk, such as management restriction eﬀects and riskshifting eﬀects attributable to moral hazard. We find supportive evidence forthe liquidity provision/capital infusion eﬀects in particular for PFI, PCA, and
DIR. Our evidence favors the adverse contagion eﬀect rather than the liquidity
provision/capital infusion eﬀects for PFI programs with multiple recipients. In
the largest PFI program, however, the restrictions on management policy ac-2companied with PFI might have aggravated the systemic risk, consistent with
Bayazitova and Shivdasani (2012). In FRS, the adverse moral hazard eﬀect tend
to oﬀset the liquidity provision/capital infusion eﬀect. We find the relatively
strong eﬀect of moral hazard in particular for the failure of small banks, because
small banks cause herding behaviors and gamble for the subsidies, consistently
with the argument of Acharya and Yorulmazer (2007a). The introduction ofblanket guarantees and the special public management mitigated the systemicrisk contribution. There are no evidence for the adverse eﬀects due to riskshifting eﬀect due to deposit insurance. Incidentally, we confirmed the positive
size eﬀect and negative VaR eﬀect on the systemic risk. Consistently with theaggregate uncertainty of the liquidity, we confirmed that the larger reserves on
the Bank of Japan (BOJ) mitigates the systemic risk by providing suﬃcientliquidity into the market, in line with Holmström and Tirole (1998) and Allenet al. (2009).
In relation to the adverse contagion eﬀect, we examine the rationale and theoutcome of too-big-to-fail (TBTF) management. O’Hara and Shaw (1990) findthe positive announcement eﬀect of the TBTF policy on the included banks.
Demirgüç-Kunt et al. (2013) argue that the limit imposed by a country’s publicfinances are reflected in bank valuation and CDS spread. Although we confirm
that the average systemic risk of the largest banks is higher than that of otherbanks and that the latter is positively associated with the former, we do notnecessarily observe the amplified eﬀects of the former on the latter. In addition,
when the regulator manages the largest distressed banks, the result does notshow clear evidence that systemic risk is calmed.
Lastly, we explore the limitations of crisis management. We observe sevendays on average that systemic risk was extremely high. We argue that management does not work eﬀectively for systemic risk in the tail when management3

should work most eﬀectively. Moreover, crisis management sometimes worsens
the systemic risk in the tail.
Many papers propose systemic risk indexes, which are introduced briefly in alater section. We follow Adrian and Brunnermeier (2011), Lopez-Espinoza et al.
(2012), and Girardi and Ergün (2013) to use the delta conditional Value-at-Risk(CoVaR) as a systemic risk index. The CoVaR on financial system measures the
maximal loss rate of the financial system conditional on the event that certainbank suﬀers severe losses beyond the VaR. The delta CoVaR is the systemicrisk contribution of distressed banks, which is defined as the standardized difference of the CoVaR between the distress and the normal state. It captures therisk spillover eﬀects from a distressed bank to the overall financial system. We
use Engle (2002)’s DCC-GARCH (generalized auto-regressive conditional heteroskedastic model with dynamic conditional correlations) model to calculate
the CoVaR.
Section 2 describes the regulators’ crisis management and our methodology for estimating CoVaR. Section 3 provides the estimation results of various
regressions that investigate the relationship between crisis management and systemic risk. In section 4, we introduce the Markov regime switching model todistinguish the extreme systemic risk state from normal state. Using the inferredstates, we examine the eﬀectiveness of crisis management during the period of
extremely high systemic risk. Section 5 discusses policy implications. Section 6
concludes the paper.
1.1. Related literature
There is a substantial empirical literature on the contagion other than listed
above. The banking panics are considered random events or the predictable
events in the literature. Gorton (1988) shows that the panics during the U.S.
National Banking Era were systematic responses by depositors to changing per-4

ceptions of risk. Bae et al. (2003) argue that contagion is predictable. Upper
and Worms (2004) argue that the failure of a single bank could lead to thebreakdown of 15% of the banking system in Germany. Furfine (2003) argues
that federal funds exposures are not large enough to cause a great risk of contagion. These two papers examine the interbank connection of the banks while
the contagious behaviors of the depositors are empirically examined in Saunders
and Wilson (1996) and Shimizu (2009b) for example. Jorion and Zhang (2009)
examine the credit contagion via direct counterparty credit risk on the asset
side.
Recently, among four crisis management measures, PFI program has attracted the interest of researchers. Veronesi and Zingales (2010), Bayazitovaand Shivdasani (2012), Li (2013), Cornett et al. (2013), Wilson and Wu (2012),
Khan and Vyas (2013), and Liu et al. (2013) investigate the outcomes of a PFI
program called troubled asset relief program (TARP) during the global financial
crisis in the United States. Shimizu (2006) and Montgomery and Shimizutani(2009) examine the PFI program during the Japanese financial crisis. However,these papers are primarily concerned with bank performance, TARP costs, orchanges in value rather than systemic risk. One exception is Lopez-Espinosa etal.(2012) investigating the eﬀect of recapitalization on systemic risk using the
CoVaR approach. Our results for PFI programs are consistent with theirs.
PCA is investigated in Aggarwal and Jacques (2001), Jones and King (1995),
Dahl and Spivey (1995), Cummins et al. (1995), and Benston and Kaufman(1997). Among others, Aggarwal and Jacques (2001) estimate the impact of
PCA on both bank capital and credit risk. Almost little evidence exists forthe third measure: a FRS. Goodhart and Schoenmaker (1995) summarize FRS
in twenty-four countries in the 1980s and 1990s. Brei et al. (2013) examine
rescue measures and the bank lending supply during the recent global financial

5

crisis. 1 The last measure, DIR act, which implements a blanket guarantee inan extreme case, is studied in Upper and Worms (2004), Kane and Klingebiel(2004), Hovakimian et al. (2003), Hanazaki and Horiuchi (2003), and Honohan
and Klingebiel (2001). Upper and Worms (2004) argue that the financial safety
net considerably reduces the danger of contagion. Hovakimian et al. (2003) consider the risk-shifting eﬀect of explicit deposit insurance. Kane and Klingebiel(2004) report the blanket guarantee in twelve countries that experienced crises.

2. Methodology
2.1. Crisis management
Our sample period is from April 1995 to March 2004. In 1995, the Japanesefinancial system experienced the failure of a bank that was viewed as the startof the subsequent financial crisis. 2 In December 2013, the last failure occurred
during the Japanese financial crisis.3 Our sample is restricted to listed banks.
Non-listed banks and other small depository institutions are excluded from oursample.
Table 1 shows the events of crisis management measures taken by the regulator for our sample banks. These events are available in the annual report of
the Deposit Insurance Corporation of Japan (DICJ) and are also documentedin Shimizu (2009a). We define the event date as its announcement date andidentify the date by searching Nikkei Telecom Database (Nikkei Degital Media,

1 See Acharya and Yorulmazer (2007a) for other unpublished works studying the failure
resolution policy.
2 Nikkei reported that the Ministry of Finance announced the failure of regional bank Hyogo
on August 30. Three years before this failure, Toho Sougo Bank failed and was rescued by Iyo
Bank. We do not include this event in our sample because of the long interval between theevents. Horiuchi and Shimizu (1998) analyze the bank behavior during the pre-crisis period
in early 1990s.
3 One regional bank Ashikaga failed after it received public capital.

6

Inc.) from one month before the reported oﬃcial date when the measure wastaken.
—————————————————————
Table1—————————————————————In standard textbooks, the systemic risk is broadly defined as any risk that
may aﬀect the financial system/market as a whole. Typically, systemic risk
surges when the losses or the failure of one bank spread to other banks. Liquidity shortages and/or heightened counterparty credit risk are strikingly observed
phenomena, because the losses generate a shortage of liquidity and the value ofthe debt obligation declines. Given the overlapping nature of financial claims,
liquidity shocks spread through contagion (Allen and Gale (2000)). In particular, Eisenberg and Noe (2001) emphasize the interdependence of banks throughinterbank market transactions. Under the multiple lending relationships prevalent in Japan, the default of large borrowers simultaneously damages more than
one bank. In addition, informational contagion occurs because the failure of
one bank serves as the signal that predicts the failure of other banks (Acharya
and Yorulmazer (2008)). Our systemic risk index, delta CoVaR, captures thepotential for such spreading of financial distress across banks by measuring theincrease in the tail co-movement.
We now explain how the regulator introduced these measures and how thesemeasures work for systemic risk. The PFI programs allow banks to reinforce
equity capital and provide liquidity to the financial system and the recipientbank. The regulator oﬀered new PFI programs several times during our sample
period. Among these programs, the largest program was introduced in 1999(#15 in Table 1). In this program, the fifteen largest banks that were considered relatively healthy but that had substantial influence over the systemic risk

7

applied for the reinforcement of equity capital. 4 The second program was in
September 1999. Four relatively weak regional banks reinforced their equity
capital. Subsequently, one or a few banks applied simultaneously for the injection program. The total number of approvals are thirteen during the sample
period.
As noted in the introduction, in addition to the liquidity provision eﬀect, theinfusion has the eﬀect of decreasing the probability of bank runs and loweringsystemic risk because it takes the form of preferred stock or debt subordinatedto deposits.

5

These eﬀects are at least enjoyed by the recipients. Further-more, appropriate PFI programs not only prevent distressed banks from going
insolvent but also prevent a contagion of failures, because they ameliorate thespillover eﬀect of the liquidity shortage (Allen and Gale (2000), Freixas et al.
(2000), Diamond and Rajan (2005), Shin (2008)). In other words, we may observe the adverse contagion eﬀect that non-recipients also enjoy lower systemicrisk when other banks participate in the PFI program.
However, the program comes with restrictions on management in Japan andin the United States. In particular, Bayazitova and Shivdasani (2011) stressthat restrictions on management compensation caused banks to refuse infusions. In Japan, restrictions on other activities rather than management compensation might trigger turmoil over systemic risk, as emphasized in Shimizu(2006). Importantly, because the regulator has an incentive and is able to makediscretionary decisions to promote loans to small and medium-sized firms under certain political pressure, recipient banks might not be able to choose the

4 The recipients were Daiichi-Kangyo, Fuji, Industrial Bank of Japan, Sanwa, Tokai, Sumitomo, Sakura, Asahi, Daiwa, Yokohama, and five trust banks. The announcement date of thisevent is the date on which the government decided to inject funds into fifteen banks. Notethat we ignore the notorious program introduced just before # 15 because its scale was small
relative to this program.
5 Even under full deposit insurance coverage, depositors may care about the temporary
inconvenience of withdrawal until the failure is fully resolved.

8

optimal amount of loans. Such a restriction may erode systemic risk, because it
delays the resolution of their failed borrowers. We call this eﬀect the management restriction eﬀect. 6
PCA requires early intervention on a timely basis when a bank’s capitalization is still positive but not-well capitalized. For example, the regulator orders
banks to recapitalize, suspend dividends, restrict asset growth, and prohibit
some or all activities (Benston and Kaufman (1997)). The regulator introduced
PCA scheme in 1998 and ordered the first PCA to one of the regional banks in
April 1999. Eight PCA events are in the sample. The scheme of PCA in Japanis similar to that of U.S., which was enacted by FDICIA in 1991.7 However, thezones of capitalization might be diﬀerent between Japan and U.S. 8 Appropriate
PCA orders lead to lower systemic risk by preventing the distressed bank fromfailing or by mitigating damages to the financial system.
However, PCA may induce other banks to increase risk ex ante (Aggarwal
and Jacques (2001), Davis and McManus (1991)). Such banks may have greater
incentives to gamble for their resurrection when facing a stringent PCA. In
addition, as Dahl and Spivey (1995) point out, capacity is limited for distressedbanks to correct positions of under-capitalization without appropriate public
capital infusion. Therefore, PCA may not work for systemic risk and may haveadverse eﬀects. We call this risk-shifting (moral hazard) eﬀects of PCA.
When a bank finally fails, deposit insurance resolves the failure, because
private-sector resolution is not always, or not usually, feasible. The regulator
usually takes P & A -like resolution policy rather than deposit payoﬀs. In such
rescue package, the failed bank is sold to another healthy bank. This rescuing

6 Increasing loans to small and medium-sized firms may have an adverse eﬀect because too
many bankruptcies of such firms trigger the bank failures.
7 See Table 1 of Benston and Kaufman (1997) for details.
8 Additionally, they are diﬀerent depending on whether banks operates abroad or not inJapan.

9bank usually purchases or assumes the assets and liabilities of the failed bankswith the aid of a subsidy provided by deposit insurance. The subsidy usually
covers the diﬀerence between the market values of the assets and liabilities.
Deposit insurance sometimes purchases part of assets and deposits of the failed
bank. Regulators seek a rescuing bank among candidate banks whose operatingarea is the same as or adjacent to the failed bank.
Among sixteen FRS, three exceptions exist.9 When two long-term credit
banks failed in 1998 and one regional bank failed in 2003, they were temporarily
nationalized.10 This scheme, oﬃcially called special public management, is abailout policy in the narrow sense. Unlike the other scheme, no value remained
to stockholders of these banks.
Similar to PFI and PCA, the FRS may also ameliorate systemic risk if it
succeeds in preventing the spillover, provides the liquidity, and eventually toisolate the banks at default from the market ( Cordella and Yeyati (2003)).
However, the scheme may create moral hazard incentives, cause herding behavior by healthy banks, and increase interbank correlation of asset returns,
because subsidies are provided only when many banks fail (Acharya and Yorulmazer (2007a)). In this case, the resolution scheme may have adverse eﬀects on
systemic risk. We call this phenomena the moral hazard eﬀect of FRS.
The blanket guarantee was practically implemented through the special fund

9 We do not distinguish between the resolution scheme of the Ministry of Finance (MOF)from that of the Financial Services Agency (FSA). The latter took the position of the department of financial regulation in the MOF after 1998. The method of the MOF was similar
to that of the FSA. However, it is worth while to stress that the failure resolution scheme
was underdeveloped and that the aid of a subsidy was implicit rather than explicit. Under
the well-known convoy system and the entry-branch regulation, the MOF could provide an
implicit subsidy in the form of favorable treatment to the bank that cooperatively rescues afailed bank. Since the subsidy was implicit and the resolution scheme was not explicitly formulated, these arrangements may be considered relatively close to the merger and acquisition
procedures of the private-sector.
10 They are Long-term Credit Bank of Japan, Nippon Credit Bank, and Ashikaga bank. In
addition, public fund injections into Resona Bank (# 41) is considered de facto nationalization
because Resona Bank issued common equity rather than preferred stock. However, we do notcount this occurrence as FRS but PFI.

10

assistance. The DICJ provides the rescuing bank with amounts of funds overthose required for deposit payoﬀs. 11 When introduced in 1996, the blanket
guarantee period was scheduled to end in March 2001. In the DIR act of 2000,
the period was extended. The blanket guarantee finally ended in March 2002
except for the settlement account (e.g. ordinary deposits). The reform of 2002
enacted this measure as permanent. 12
When insurance coverage extends to all liabilities, the market expects thatcreditors do not incur losses when banks fail at the cost of the regulator andtaxpayers. Therefore, the blanket guarantee may ameliorate the systemic riskin the sense that the insolvency of one bank does not lead to a liquidity shortage of any bank, borrower, and depositor. However, as in PCA, the blanket
guarantee may also have adverse eﬀects on systemic risk, because creditors lose
the incentive to monitor banks and banks can shift risk onto the insurer (Hovakimian et al. (2003), Marcus and Shaked (1984)). This phenomenon is called
the risk-shifting eﬀect of deposit insurance.

2.2. Econometric method of delta CoVaR
Many candidates exist for the systemic risk index. Acharya et al. (2010)
propose the systemic expected shortfall (SES) and marginal expected shortfall (MES). Lopez et al. (2014) propose the CoMargin, which systematicallyadjusts collateral requirements on the basis of the CoVaR concept. Huang etal. (2009) propose the “distress insurance premium” indicator, which measures

11 In addition to the blanket guarantee, the DICJ began to collect special insurance fees in
addition to ordinary fees. The total fees became almost seven times as large as the previous
ones. The reform also enabled the DICJ to purchase depository claims of failed banks throughits subsidiary.
12 The reform of 1997 was somewhat minor. The framework for new mergers and assistance
was introduced but only used for one resolution. The reform of 1998 introduced the receivership of the failed banks, the establishment of a bridge bank, and the temporary nationalizationof failed banks.

11the expected portfolio loss above the total liabilities. Lehar (2005) proposes
the systemic risk index on the assets and the number of banks measured as
the probability of systemic crisis. Billio et al. (2012) propose the interconnectedness measure using the principal component analysis. De Jonghe (2010)
proposes tail-β measure using extreme value analysis. Each of these measures
has advantages and disadvantages. We employ the CoVaR measure simply because VaR is the most familiar concept among the indexes measuring the riskof loss.
The delta CoVaR is estimated in three steps. In step 1, we calculate thedaily market return of bank assets using the option pricing formula. In step2, we estimate the parameters of the bivariate normal distribution of returns
for the financial system and each bank by multivariate GARCH model withdynamic conditional correlation. In step 3, we estimate VaR, CoVaR, and delta
CoVaR using the estimated parameters in step 2.
In step 1, we calculate market value of asset because the asset VaR is more
relevant when we study the systemic risk. When we use equity VaR, the put
option value of deposit insurance is ignored. Since regulator’s crisis managementaﬀects this put option value in various points, we use asset VaR instead ofequity VaR. The specific procedure of the step 1 is as follows; The gross returnof the bank j at date t = (1, · · · T ) is defined as Rjt = ln Pjt − ln Pj,t−1 ,where Pjt is the stock price. We estimate asset return Xjt using Black-ScholesMerton formula. Define bank equity value as VE , asset value VA , debt value(including deposit insurance) as B, and risk-free discount rate as r. Then,the market value of equity satisfies the formula (Merton (1974, 1977, 1978))√2
VE = VA N (d1 ) − Be−rT N (d2 ) , with d1 = {ln(VA /X) + (r + σA/2)T }(σA T )√and d2 = d1 − σA T , where σA is the volatility of asset value. Using thisformula, we are able to calculate market value of asset on the daily basis. Our

12method follows one used in Vassalou and Xing (2004). 13 Asset return is definedas Xjt = ln VAjt − ln VA,j,t−1 . We also define the asset return of financial system∑∑
as XSt = ln j VAjt − ln j VAj,t−1 . Subscript S denotes financial system.
The second step is as follows; We assume that each pair of individual asset
return and system return follows bivariate GARCH model with DCC.

Xtj = µjt + ϵjt(1)j, where Xtj = (XSt , Xjt )′ is the j-th pair of asset return vector, µjt = α0j +α1j Xt−1

is the conditional drift term, ϵjt is the error term. This error term follows
ϵjt = (Htj )1/2 νtj(2), where νtj follows bivariate i.i.d. joint normal distribution N (0, I). The conditional covariance matrix of ϵjt defined as Ht = Et−1 (ϵjt ϵj′t ) is decomposed into
1/2

1/2

Ht = Dt Rt Dt , following Engle (2002). Dt is a diagonal matrix with element2
being conditional variance of j-th return σjt. Rt is time-varying correlation co-eﬃcient matrix with 1 on the diagonal and ρjS,t oﬀ the diagonal.
The variance - covariance matrix of ϵjt is modeled as
Rt = diag(Qt )−1/2 Qt diag(Qt )−1/2)(
Qt = (1 − λ1 − λ2 )R + λ1 ϵ̂t−1 ϵ̂′t−1 + λ2 Qt−1

(3)
(4)

√
The typical element of Qt is qjS,t satisfying ρjS,t = qjSt / qjjt qSSt . ϵ̂t−1 is the

13 The method consists of the following six steps. (1)we estimate σ
Et , standard deviationof Rjτ (τ = t − 250, · · · , t ) for each t, (2) Substituting this σEt as initial value, we compute
VAt using the formula for past 12 months, (3): we estimate σAt using daily data VAt in (2)for the past 12 months, (4) Using σAt in (3), compute VAt using the formula for the past
12 months, (5) we repeat (3) and (4) until σAt from two consecutive iterations converge, (6)Using converged σAt , compute daily VAt from the formula.

13

−1/2

standardized error defined as Dt

ϵt . R is quasicorrelation matrix. λ1 and λ2

is nonnegative parameters satisfying 0 ≤ λ1 + λ2 < 1. The estimates of µjt andvariance covariance matrix Ht are obtained by maximal likelihood estimation
method.
The third step is as follows; The CoVaR is defined as()
P r XSt ≤ CoV aRtSj | Xjt ≤ V aRtj = q(5), where q is the confidence level. Following Girardi and Ergün (2013), thisconditional bivariate normal probability is transformed into joint probability()
P r XSt ≤ CoV aRtSj , Xjt ≤ V aRtj = q 2 .

(6)

The benchmark state is defined as the one sigma region around the conditionalmean {µjt − σjt ≤ Xjt ≤ µjt + σjt }. The benchmark CoVaR is defined as()
P r XSt ≤ CoV aRtB Sj , µjt − σjt ≤ Xjt ≤ µjt + σjt = pjt q(7)

with pjt defined as P r ( µjt − σjt ≤ Xjt ≤ µjt + σjt ) = pjt . Finally, delta CoVaR
is defined as

Sj
Sj∆CoV aRtSj = 100 × (CoV aRtSj − CoV aRB,t)/CoV aRB,t(8)

The delta CoVaR represents the systemic risk contribution of the distressedbank relative to that of the normal state.
2.3. The baseline regression
We employ daily data on equity prices and the market value of equity fromthe Nikkei Needs Database. The book value of debt is available quarterly, semi-

14

annually, or annually. Book value data are collected from the EoL database
and the Nikkei Needs Database. Our basic hypothesis is that the systemicrisk contribution of a particular bank decreases when the regulator takes crisis
management measures. Our baseline regression equation is defined as∆CoV aRtSj = xjt β + Djt θ + uj + vjt ,(9)where xjt is a vector of covariates for bank j on date t. Following Adrian andBrunnermeier (2011) and Lopez-Espinosa et al. (2012), we examine volatility
in the stock market (Tokyo Stock Exchange), the change in the 10-year JGB
rate, the short-maturity yield spread between the overnight call rate and thethree-month CD rate, the long-maturity yield spread between the three-month
CD rate and the 10-year JGB rate, and the market return (TOPIX). Because
no volatility index available existed during the period, stock market volatility
is measured as the daily standard deviation of the TOPIX return for the priorweek. In addition to these covariate variables, we include VaR, log of asset
size, and leverage of each bank, following Girardi and Ergün (2013). Lastly, we
include two monetary policy variables, the call rate and the reserves on the BOJ
account.
The vector of the dummy variable Djt are the set of dummies corresponding
to each crisis management measure. This variable takes the value of 1 during thecorresponding period of measures taken and 0 otherwise. The crisis management
event period is 30 days, which starts from the event date of announcement. The
individual error term uj and the idiosyncratic error vjt are included in the priorequation.

15

3. Empirical analyses on systemic risk and crisis management
3.1. Four types of crisis management and systemic risk
Figure 1 shows the time series of the cross sectional average of delta CoVaR
at the 5% tolerance level. 14 The vertical lines show the approximate date of theeight major events. Among them are the introduction of the blanket guarantee(#3), the largest PFI(#15), the extension of the blanket guarantee (#27), andthe failure of one of the largest banks (#5 and #40). Although these lines andthe peaks of the delta CoVaR do not coincide precisely, the peak is sometimes
found just around the event date.
—————————————————————
Figure 1—————————————————————
Table 2 summarizes the cross-sectional averages of delta CoVaR by year andtype of crisis management. The sample mean over the full period is approximately 22%. The 5 and 95 percentiles are 7.7 and 47.5, respectively. The
mean was the highest in 1997, and the second highest in 2000. The lower panel
compares the summary statistics by type of crisis management. First, the subsample mean of crisis management is smaller than that of no crisis management.
Second, the subsample means of PFI and PCA are smaller than that of no crisis
management, respectively. These medians show similar tendencies.
—————————————————————
Table 2—————————————————————
Table 3 shows the estimation results of equation (9) in two specifications
when four dummies are used. First, the coeﬃcients of PFI and PCA are signif-

14 The average delta CoVaR is used in Gauthier et al. (2012) with a slightly diﬀerent
definition. See equation (9) on page 600.

16

icantly negative. The systemic risk contribution of the distress of a particularbank declines when the regulator announced either PFI or PCA. The results
provide supporting evidence for the liquidity provision/capital infusion eﬀects
of these two measures. The significantly positive coeﬃcients of FRS suggest
the moral hazard eﬀect. The DIR dummy has no significance in both specifications, suggesting that the eﬀect of preventing a liquidity shortage is oﬀset by
the adverse risk-shifting eﬀect.
—————————————————————
Table 3—————————————————————
Among the control variables, volatility, yield slope for long maturity, market
return, and log of assets have significantly positive impacts on the delta CoVaR.
The coeﬃcients for change in JGB rate, short maturity yield spread, VaR,
call rate, and log of reserves are significantly negative. These signs are mostly
consistent with the intuition and the results in Adrian and Brunnermeier (2011),
Lopez-Espinosa et al. (2012), and Girardi and Ergün (2013). Among them, we
confirmed the positive size eﬀect and negative VaR eﬀect on systemic risk.
The results on the call rate and BOJ reserves are highly contrasting andinteresting. When a lower call rate prevails, the systemic risk contribution
increases. However, the BOJ reserve has the opposite sign, which may have
implications for the quantitative easing policy that began in March 2001. The
larger reserves mitigate systemic risk by providing suﬃcient liquidity to themarket, consistently with the arguments of aggregate uncertainty in Holmströmand Tirole (1998) and Allen et al. (2009).

3.2. Individual measures and systemic risk
Table 4 shows the estimation results when forty-two individual event dummies are used. First, eight PFI events have negative impacts on the systemic17risk contribution, whereas two have the opposite eﬀect. Surprisingly, the largest
program (# 15) has a positive impact on systemic risk. The recipients of thisprogram were the largest banks and those of other programs were mostly smaller
regional banks. The largest banks were healthier than other banks with respect
to the capital asset ratio. This result provides evidence for the management
restriction eﬀect that restrictions on management policy accompanied by PFI
would delay the resolution of non-performing loan problems, and that the probability of successive failures would increase. The six coeﬃcients of PCA are
significantly negative. The results of these two measures are mostly consistent
with the results shown in Table 3.
However, the results of two other measures are quite diﬀerent. The eﬀects
of FRS become ambiguous with four being significantly positive and five significantly negative. This result may suggest that market opinions for the resolution
scheme tend to be divided. In the FRS, the adverse moral hazard eﬀect tends
to outweigh the liquidity provision/capital infusion eﬀect, but not in PCA and
PFI. This relatively strong moral hazard eﬀect might be reasonable, because
the market might expect that other small banks with similar characteristics
fail when a small bank fails. Those banks cause herding behavior and gamble
for subsidies, as suggested in Acharya and Yorulmazer (2007a). Furthermore,among three nationalizations, the first two have no significant eﬀects.
Lastly, three of the DIR dummies have significantly negative coeﬃcients. In
contrast to the result in Table 3, the systemic risk contribution of the distressof a bank is mitigated by reforms in 1996, 1998, and 2002. The introductionsof a blanket guarantee and special public management mitigated the systemicrisk contribution. No evidence is found for the adverse eﬀects attributable torisk-shifting.
—————————————————————

18

Table 4—————————————————————

3.3. Direct and indirect spillover eﬀect
To this point, we supposed that the eﬀect of crisis management on systemicrisk is not diﬀerent across banks regardless of whether or a specific bank is
directly aﬀected by the measure. Except for the DIR, these management measures generally have direct and indirect eﬀects. Among the three measures,
because the PFI measure has multiple recipients, it is suitable in investigatingsuch heterogeneous eﬀects. Capital infusion not only prevents insolvency of therecipients but also prevent contagion of failures. By adding the new dummy
variable to equation (9), we distinguish the liquidity provision/capital infusioneﬀect from the adverse contagion eﬀect.
The dummy ckjt which takes the value of 1 if j-th bank is the recipient of
capital injection program k and 0 otherwise, is added to equation (9). Thektakes the value of 1 during the event period of program k fordummy Djt

any j and 0 otherwise. The former measures the liquidity provision/capitalinfusion eﬀect, which is a direct spillover eﬀect specific to the recipient, and thelatter measures the adverse contagion eﬀect, which is an indirect spillover eﬀectcommon to all banks when program k is taken.
—————————————————————
Table 5—————————————————————
According to Table 5, diﬀerences exist between the direct and indirect eﬀects
in four events. In the largest injection program (#15), the coeﬃcient for the
direct spillover is significantly positive. The banks that applied for the injection increased their contribution to systemic risk more than their counterparts.

19This result is consistent with the previous view that, the market expected, management restrictions might delay the resolution of the failed borrowers of therecipients. However, the indirect eﬀect also becomes positive, which might bereasonable, because a surge in the systemic risk of these banks may trigger an
overall increase in systemic risk.
In event #32, the direct spillover aggravates systemic risk. However, in two
events (#25, 28), the direct spillover is significantly negative and the diﬀerences
are not found in other two events (#22, 34). The indirect eﬀects are negative
except for the event (#15), which is consistent with the previous results. Thus,
our results are ambiguous for the diﬀerences between the direct and indirect
spillovers. Our evidence favors the adverse contagion eﬀect rather than liquidity
provision/capital infusion eﬀect for multiple PFI programs. These results may
reflect the existence of the management restrictions eﬀect.
3.4. Too-big-to-fail and systemic risk
We further investigate PFI program in 1999 (#15), because the adverse
eﬀect was found in the previous tables. This investigation also provides us
with an opportunity to evaluate the relationship between the TBTF policy
and the systemic risk, because the recipients were the largest banks in Japan.
The rationale for the TBTF policy is that the large banks have a significant
influence over systemic risk. This rationale also supports the new regulation on
globally systemically important financial institutions (G-SIFIs) and/or globally
systemically important banks (G-SIBs). Some recipients of this program (#15)
are now forming the largest financial groups, three of which are identified as
G-SIBs (Mitsubishi UFJ FG, Mizuho FG, and Sumitomo Mitsui FG).
In Table 3, we confirmed the size eﬀect of the delta CoVaR. We take a stepfurther, and consider that the average delta CoVaR of the largest banks aﬀects
the delta CoVaR of other banks. The largest banks are defined as the city banks

20and long-term credit banks.15 To disentangle the influential eﬀect of the largest
banks, we use the two-step estimation method. In the first stage, we estimate
the delta CoVaR of the largest banks, using a subsample of these banks. Then,
we predict the daily average of these delta CoVaRs, which is called the largest
banks’ delta CoVaR. In the second stage, we estimate eq. (9) by adding thelargest banks’ delta CoVaR.
In addition to event $15, we examine the events to which one of the largest
banks is related. These events are events #5, #8, #13, #14, #40, and #41.16
In these estimations, we use a subsample consisting of 30 days before and after
each of the event date. We define a crisis management dummy which takes thevalue of 1 after the event and 0 otherwise, and use the cross term of the largest
banks’ delta CoVaR and the crisis management dummy as the regressor.
We consider two TBTF hypotheses. The first hypothesis is that the largest
banks’ delta CoVaR has amplified eﬀects on the delta CoVaR of other banks.
Statistically, the coeﬃcient of the largest banks’ delta CoVaR is predicted to begreater than 1. The second hypothesis is that crisis management related to one
or some of the largest banks has an ameliorating eﬀect on the delta CoVaR ofother banks.
—————————————————————
Table 6—————————————————————
Table 6 displays the estimates of the second stage. The coeﬃcients of the

15 They are Daiichi Kangyo (Mizuho), Hokkaido Takushoku, Tokyo, Sakura, Mitsubishi
Tokyo UFJ (Mitsubishi, Mitsubishi Tokyo), Fuji (Mizuho), Sumitomo (Mitsui Sumitomo),
Daiwa (Resona), Sanwa (UFJ), Tokai, Asahi, Industrial Bank of Japan, Long-term Credit
Bank of Japan (Shinsei), Nippon Credit Bank (Aozora), Mitsubishi UFJ FG, Resona Holdings,
Mitsui Sumitomo FG, Mizuho FG.
16 #5 and #8: Failures of Hokkaido Takushoku Bank, #13: Failure of Industrial Bank ofJapan, #14: Failure of Nippon Credit Bank, #40:Failure of Resona Bank, #41: PFI of Resona
Bank. In #5, the merger by the rescuing bank was canceled. After two months, the assets of
Hokkaido Takushoku were sold to other rescuing banks. See also Shimizu (2009a) for moredetails.

21

largest banks’ delta CoVaR are mostly significantly positive and are greaterthan 1 for the three events (#5, #8, and #15). These amplified eﬀects of
the largest banks’ systemic risk support the first TBTF hypothesis. However,
we find no amplified eﬀects in the other four events. In the lower panel, we
report the subsample means of the delta CoVaRs, before and after the events
depending on whether they are the largest banks or other banks. Apparently,
the delta CoVaRs of the largest banks are greater than those of smaller banks,
whose diﬀerences are statistically significant, both before and after the event.
Therefore, although the largest banks’ delta CoVaR is influential in that they
are higher than the average of other banks, we do not necessarily observe theamplified eﬀects of the largest banks’ systemic risk.
At the bottom of Table 6, we see the statistically significant diﬀerences ofthe subsample means for smaller banks before and after the events related to
the largest banks. However, we find no clear evidence of the second hypothesis.
Two coeﬃcients of the cross term of the management dummy and the largest
banks’ delta CoVaR are significantly positive, two are significantly negative, andthe other three are not significant. We observe no systematic change after the
management measures are taken.

4. Extreme systemic risk state and delta CoVaR
4.1. Markov regime switching model and systemic risk
The systemic risk is most serious when the delta CoVaRs are extremely high,i.e., in the tail. We consider the daily average of the delta CoVaR:

ADCt =∑∆CoV aRtSj /Nt

j

22

(10)

as the system wide risk representing the degree of comovements in the tail, where
Nt is the number of banks. Crisis management should work most eﬀectively forsuch states.
The system-wide state of extreme systemic risk is identified by the Markov
regime-switching model by Hamilton (1989). We consider the three states,
st = {1, 2, 3} with the transition probability πtij from i to state j. We infer the probability of state i P r(st = i | ADCt , . . . , ADCt−3 ) given the available
information. We specify the model by assuming that each regime diﬀers in theirmeans of ADCt , which corresponds to the intercepts and the three lags of ADCt
in the real equation.
In the same way, we also consider the state identification for the averagedelta CoVaR with a negative sign.

ADCtn =∑

∆CoV aRtSj /Ntn ,(11)j∈∆CoV aRtSj <0

where Ntn is the number of banks with negative delta CoVaRs. This investigation is motivated by the finding in Bae et al. (2003) and Lopez-Espinosa etal. (2012). The former argue that the evidence that contagion is stronger for
extreme negative returns than for extreme positive return is mixed. The latterargue that asymmetries based on the sign of bank returns play an importantrole in capturing the sensitivity of systemic risk. Allen et al. (2012) also argue that extremely high levels of systemic risk in the banking sector impact
the macroeconomy. Instead of return, we examine the negative average delta
CoVaR. As Table 2 shows, the ADCs themselves are positive. However, manydelta CoVaRs have a negative sign. Even if it is negative, a large absolute value
indicates that the system-wide influence cannot be ignored.
The delta CoVaR can be negative when the returns of bank j are negatively
correlated with the system returns. Suppose that the market perceives that crisis
23management succeeds in the sense that the financial system becomes relatively
more stable. Then, the return of this bank may continue to worsen each until
the exit, whereas the market return of the financial system may improve. In
this case, as the bank becomes more distressed, the absolute value of the CoVaRof the financial system becomes smaller. Then, we may have a negative delta
CoVaR. The states for negative delta CoVaR are defined as the state 4, 5, and
6. Regime switching is estimated for a negative delta CoVaR, independently of
the regimes {1, 2, 3} to avoid complexity.
The upper panel of Table 7 shows the coeﬃcients of intercepts and the lagsof ADC. In the lower panel, we report the Markov transition probability fromstate to state. Among states {1, 2, 3}, the intercept is the greatest for state
1. Among states {4, 5, 6}, the intercept has the largest absolute value for state
6. We call the former an extreme positive systemic risk state and the latter an
extreme negative systemic risk state. If the state was 2 yesterday, the probability
that the state is 1 today is 1.2%. If the state was 4 yesterday, the probability
that the state is 6 today is 2.8%. In such sense, both states correspond to thetail in each of Markov process.
—————————————————————
Table 7—————————————————————
We identify the inferred state at t as the most probable state;ŝt = max P r(st = i | ADCt , . . . , ADCt−3 )i(12)Using this, we identify the positive and negative extreme systemic risk period
as T P = {t : ŝt = 1} and T N = {t : ŝt = 6}, respectively. In the bottom of thetable, we report the frequencies of the inferred states.

24

4.2. Crisis management during extreme systemic risk period
In Table 8, we investigate whether crisis management works more eﬀectively in the tail. The upper panel indicates the number of days with a positive/negative extreme systemic risk and with crisis management. We report thedays for each year and their total. We observe that a positive extreme systemicrisk state is most frequent in 1996. On average, seven extreme states occur
during a year. However, because they are the tail events, a small number ofdays has an extreme state.
In the regression analyses, we do not distinguish each crisis management
measure. The crisis management dummy takes the value of 1 if a management
measure is taken. Another dummy is defined to represent a period of extreme
systemic risk and takes the value of 1 if t ∈ T P = {τ : ŝτ = 1} or t ∈ T N ={τ : ŝτ = 6}. These two dummies are crossed to generate eight dummies.
Two dummies are excluded to avoid perfect collinearity, which are no crisis
management under normal state with respect to positive and negative states.
In the middle panel, we report the sensitivities of the six dummies. In thefirst column, we estimate eq. (9) using these dummies for the entire period.
The sensitivity of the crisis management in the tail is higher relative to thoseof no crisis management under the normal systemic risk ((A) or (D)). In addition, the sensitivity of crisis management under normal systemic risk is lower
than no crisis management under the same condition ((B) or (E)). The lower
panel reports the test statistics for the equality of the sensitivities. In the tail,the sensitivity of crisis management is not statistically diﬀerent from that of nocrisis management ((A) = (C), (D) = (F)). Thus, crisis management does not
eﬀectively work for systemic risk in the tail. In addition, given crisis management, we confirm that the sensitivity in the tail is statistically diﬀerent fromthat of the normal state ((A) ̸= (B), (D) ̸= (E)).

25

To check robustness, we consider the yearly estimation using the generalized
method of moments (GMM). The sensitivity signs have approximately similartendencies as those of the first column. However, the signs of crisis management
under the normal states become ambiguous. In 1996 and 1999, at the tail of both
positive and negative systemic risks, the sensitivity of the crisis management isstatistically higher than that of no crisis management. This result may suggestthat the crisis management sometimes worsens the systemic risk in the tail.
—————————————————————
Table 8—————————————————————

5. Discussions: Policy implications for future crisis management
In summary, our analyses mostly provide supportive evidence for the liquidity provision/capital infusion eﬀects and the adverse contagion eﬀects of crisis
management. However, we also find a few exceptions, such as the moral hazard
and the management restriction. There is little evidence on the amplified eﬀects
of the spillover and on the eﬀectiveness during the extreme systemic risk period.
In reality, the regulators managed the Japanese financial crisis through trial anderror. Therefore, the results might be surprising to some of the readers. One
should be very careful when applying these results to future crisis management
for the following reasons. First, our results are limited in that we examine only
a relatively short period after the announcements. It is diﬃcult for us to capture
the long-run eﬀects because we experience the successive failures and management events during the crisis. Second, information on some of the FRS and/or
the DIR acts acts under legislation were reported in the newspapers before theannouncements. Identification of the event date is crucial for our analyses.
Third, our sample only comprises listed banks. Many non-listed banks with26

stocks that does not trade on exchanges and credit cooperatives that are notincorporated exist. In particular, many failures of very small credit cooperatives
occurred during the Japanese financial crisis. Because these cooperatives arevery small and the transmission of volatility through stock market is cut oﬀ,
the spillover eﬀects of each institution may be also considered small. However,the contagious failures may result from small shocks (Cifuentes et al. (2005)).
In addition, as Acharya and Yorulmazer (2007b) stress, the too-many-to-failproblem might be important during a crisis, because crisis management maytrigger successive failures through herding.
Fourth, in relation to the first point, the fiscal cost of deposit insurance andthe long-run eﬀects of bailout should be considered when designing a proper
crisis management scheme. According to the Annual Report of the DICJ, theamount of reserves (accumulated amount of insurance fees) fell into a deficit
in 1996 and recovered to surplus eventually in 2010. The deficit was financed
through government bonds and guarantees granted by the government, whichamounted to 17 trillion yen (Shimizu (2009)). In the long-run, soft bailout
schemes are usually criticized, because they may invoke risk-shifting moral hazard behavior (Cordella and Yeyati (2003)). However, in reality, more important is that regulatory policy may distort the long-run eﬃciency of financial
institutions under the weak governance of stockholders in Japan. Because theregulators are primarily concerned with prudence from the viewpoint of depositors, which is called the representative hypothesis in Dewatripont and Tirole(1994), weak governance may sacrifice eﬃciency, along the line with Hanazaki
and Horiuchi (2003). The low eﬃciencies of Japanese banks might suggest thatthe management may believe that it can be bailed out by being merely prudent.
The proper compensation schemes should be accompanied by crisis management(Osano (2002)).

27

The Basel III proposed macroprudential regulation frameworks from theviewpoint of the importance of systemic risk (Gauthier et al. (2012), Tarashev
et al. (2009)). Except for deposit insurance, the regulations and crisis managements might not be aimed at the system level, but, instead, at the individualbank level during our sample period. We did not have any reliable measureof systemic risk on which regulators base crisis management. As Figure 1 suggests, the several peaks of systemic risk do not seem to coincide with events
that are considered influential. Under the macroprudential capital regulation, if we could measure the systemic risk more precisely, intensively managing acrisis might become less necessary.

6. Conclusion
This paper examined the relationship between systemic risk contribution
and the four types of crisis management during the financial crisis in Japan.
We find empirical evidence that the liquidity provision/capital infusion as crisis
management helped calming down the systemic risk. However, in some cases,
there are the adverse eﬀects due to the management restrictions and the moral
hazard. The systemic risk diminishes for non-recipients of PFI programs as well.
We also find the rationale for the TBTF policy, but do not find clear evidence forthe amplified eﬀects. In addition, the eﬀectiveness of crisis management disappears in the tail of systemic risk. Thus, crisis management played the importantrole in stabilizing systemic risk during the financial crisis, but its eﬀectiveness islimited, depending on the imposed restrictions and the circumstances in which
the method taken. The analyses suggest that it is necessary to have the crisis
management method properly stabilizing the financial system.
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32

Table 1: Events of crisis managements
Event id
1
2

Year
1995
1996

3
4
5
6
7
8
9
10
11

Event date Category
19950830 Failure
19960330 Failure

Institutions
Regional bank (Hyogo)
Regional bank (Taiheyo)

19960619 Deposit insurance act reform

1997

1998

19961121 Failure
19970906 Failure
19971009 Failure
19971014 Failure
19971117 Failure
19971126 Failure
19971213 Deposit insurance act reform
19980515 Failure

1219981003 Deposit insurance act reform

13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42

19981023 Failure
19981212 Failure
19990313 Public funds injection
19990408 Failure
19990412 Prompt Corrective Action
19990522 Prompt Corrective Action
19990601 Prompt Corrective Action
19990629 Prompt Corrective Action
19990705 Prompt Corrective Action
19990914 Public funds injection
19991126 Public funds injection
20000210 Public funds injection
20000225 Public funds injection
20000428 Prompt Corrective Action
20000524 Deposit insurance act reform
20000901 Public funds injection
20000906 Public funds injection
20000928 Prompt Corrective Action
20010302 Public funds injection
20010309 Public funds injection
20010323 Public funds injection
20011127 Public funds injection
20011228 Failure
20020104 Prompt Corrective Action
20021212 Deposit insurance act reform
20030220 Failure
20030401 Public funds injection
20030517 Failure
20030611 Public funds injection
20031206 Failure

1999

2000

2001

2002
2003

Regional bank (Hanwa)
City bank (Hokkaido Takushoku)
Regional bank (Fukutoku and Naniwa)
Regional bank (Kyoto Kyoei)
City bank (Hokkaido Takushoku)
Regional bank (Tokuyo City)

Notes

Special assistance (Blanket guarantee),Special insurance fee, Repurchase of
deposittory claims
Order of suspending operation
Merger cancellation
MergerOperation transderred

Assistance for special merger
MergerReceiver, bridge bank, and special
public management (temporary
Long-term bank (Long-Term Credit Bank of Japan) NationalizedLong-term bank (Nippon Credit Bank)
Nationalized
fifteen institutions
Regional bank (Kokumin)
Regional bank (Kofuku)
Regional bank (Hokkaido)
Regional bank (Tokyo Sowa)
Regional bank (Namihaya)
Regional bank (Niigata Chuo)
four institutions
Regional bank (Kumamoto Family)
Long-term bank (Long-Term Credit Bank of Japan)
Regional bank (Hokkaido)
Regional bank (Chiba Kogyo)
Extending the period of blanket guarantee
two Regional banks (Chiba Kogyo, Yachiyo)
Long-term bank (Nippon Credit Bank)
Regional bank (Senshu)
Regional bank (Kansai Sawayaka )two Regional banks (Kinki Osaka, Higashi Nihon )Regional bank (Gifu)
three Regional banks (Fukuoka City, Kyushu, Wakayama )Regional bank (Ishikawa)
Regional bank (Chubu)
Blanket guarantee of account for settlement
Regional bank (Chubu)
Regional bank (Kanto Tsukuba)
City bank (Resona)
Nationalized
City bank (Resona)
Regional bank (Ashikaga)
Nationalized

Regional bank (Hanshin Midori)(Note): PFI (public fund injection program), PCA (prompt corrective action), FRS (failure resolution scheme), DIR(deposit insurance act reform). Sample
period : Apr. 3rd, 1995-Mar. 31, 2004. Event day is identified by Nikkei Shimbun. (Source): Annual report of Deposit Insurance Corporation in Japan.

Table 2: Summary statistics of delta CoVaR
Year

Cross sectional average of Delta CoVaR for each year

Number of banks

1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
Full sample period
Crisis management
None
Four types
PFI
PCA
Fail
DIR

108
108
107
107
104
103
101
93
91
89

Mean

S.D.

5%

Median

95%

20.3
21.4
38.1
25.0
14.6
25.2
19.0
23.6
14.8
17.7
22.0

7.2
13.0
21.7
10.6
15.6
16.9
11.4
23.0
17.1
7.6
14.4

12.9
10.4
17.8
14.0
-9.1
7.5
6.6
5.3
4.0
8.0
7.7

18.8
19.6
30.9
22.5
15.2
20.6
16.6
17.8
12.9
16.8
19.2

31.6
35.9
84.7
44.8
41.8
62.4
43.2
70.1
30.0
30.1
47.5

Mean

S.D.

5%

Median23.6
19.5 ***
19.7 ***
12.9 ***
21.9
22.1

17.9
15.1
15.3
19.0
13.1
9.8

7.8
-2.8 ***
5.8-11.5 ***
7.7
6.1

19.7
17.2 ***
15.1 ***
10.3 ***
19.8
20.6

Numberof days
186
247
245
247
245
248
246
246
245
60
221.5

Numberof days56.1781558
45.585 ***657
58.553205
45.58512841.245 **230
38.941
9495%(Note) Sample period : Apr. 3, 1995- Mar. 31, 2004. Table shows mean, standard deviation (S.D.), 5 percentile,
median, 95 percentile. Number of days is on operating basis. The results of significance test on the difference ofmeans, 5%, 50%, and 95% are reported. *, **, *** denotes the significance level of 10, 5, 1%, respectively.

Table 3 : Delta CoVaR and four types of crisis management:
Panel data estimation
Dep. Var.
Market variables
Volatility
Change in JGB rate
Yield spread (Long)
Yield spread (Short)Market return

Delta CoVaR(i)
5.475***(0.770)-15.18*(8.087)4.448***(0.974)-1.316(3.084)15.43*(8.153)(ii)
4.612***(0.899)-6.442**(2.844)4.930***(1.420)-7.337**(3.694)15.73*(8.753)

Bank variables-100.5***(26.55)12.25***(3.152)52.83(50.80)VaR
Log of asset
Leverage
Monetary policy variables
Call rate-7.267***(2.689)-4.733***(1.287)Log of Reserve
Crisis management variables
PFI
PCA
FRS
DIR
Constant

Observations
Number of bankStd. Dev. of Individual error
Std. Dev. of Idiosyncratic error
Rho
Wald Chi (zero coeffs)
p-value-3.756***(1.150)-11.16***(2.846)1.454(0.989)-0.451(1.357)
11.85***(3.264)-5.317***(1.232)-12.27***(3.054)2.226**(1.086)-1.331(1.561)-171.6**(76.14)

138,104
80
22.24
58.61
0.126
113.9
0.00

109,612
63
11.96
49.67
0.0548133.6
0.00(Notes) The random effects panel data models are estimated. Reported inparentheses are robust standard errors. *, **, or *** denotes 10%, 5%, 1%
significance level, respectively.

Table 4 :Delta CoVaR and individual measures of crisis management
Dep. Var.: Delta CoVaR
Event Type Coef.
1 F -11.07***(2.027)2 F 22.95***(6.550)3 D -8.102***(2.320)4 F -7.510***(2.645)5 F -1.104(3.214)
6 F -11.24***(3.330)7 F 3.013(3.001)
8 F 1.852(3.676)9 F 9.741***(1.743)10 D 2.626(1.826)
11 F 3.574(4.612)12 D -6.710***(2.120)13 F 2.251(1.675)14 F -2.401(2.557)15 I 9.701***(3.650)

Event Type Coef.
16 F 18.97***(5.157)
17 P -8.759(6.996)
18 P -12.68**(6.011)
19 P -18.62***(5.710)20 P -14.98***(3.243)21 P -25.50***(5.389)22 I -18.90***(3.068)23 I -5.259***(1.980)24 I 2.292(2.042)25 I -12.97***(2.028)26 P 10.20*(5.393)27 D 3.970(4.173)28 I -16.50***(4.098)29 I 3.687(3.479)30 P -11.30***(2.329)Event Type Coef.
31
I -23.54***(7.204)32
I -6.390(6.838)33
I 23.34***(6.756)34
I -8.567***(1.975)35 F 1.527*(0.797)36 P -9.105***(1.760)37 D -8.137***(1.606)38 F -6.254***(2.356)39
I -6.397***(2.289)40 F -2.234(1.890)I -5.502***41(1.265)42 F -6.879***(2.276)

Event / Var.
Volatility
Change in jgb rate
Yield spread (Long)
Yield spread (Short)Market return
VaR
Log of asset
Leverage
Call rate
Reserve
Constant

Observations
Number of bankStd. Dev. of Individual error
Std. Dev. of Idiosyncratic
Rho
Wald Chi (zero coeffs)
p-valueCoef.
3.821***(0.885)-5.447*(3.060)3.448**(1.587)-12.90***(4.414)
10.96(7.279)-94.72***(24.94)11.97***(2.731)
39.84(52.69)-6.023**(2.441)-4.813***(1.353)-150.1**(72.17)
109,612
63
9.726
49.26
0.03753983
0(Notes) Types of crisis management are public fund injection program (I), prompt corrective action (P), failure resolution scheme (F), anddeposit insurance act reform (D). The random effects panel data models are estimated. Reported in parentheses are robust standard errors.
*, **, or *** denotes 10%, 5%, 1% significance level, respectively.

Table 5 : Delta CoVaR and direct/indirect spillover: Panel data estimation
Dep. Var.= Delta CoVaR
Event
Indirect spillover dummy
Direct spillover dummy

Observations
Number of bankStd. Dev. of Individual
Std. Dev. of Idiosyncratic
Rho
Wald Chi (zero coeffs)
p-value

15

22

25

28

32

34

10.81***(4.073)21.24**(9.587)-16.81***(3.109)5.312(4.890)-9.178***(1.978)-39.57***(1.655)-12.22***(3.082)-10.07***(2.925)-8.886***(2.697)5.822**(2.631)-6.582***(1.909)2.671(2.257)

109,612
63
11.94
49.74
0.0545214.8
0109,612
63
11.64
49.74
0.0519130.5
0109,612
109,612
63
63
11.97
11.79
49.75
49.75
0.05480.05329.900e+06 1.433e+06
00109,612
63
11.95
49.76
0.054612691
0109,612
63
11.99
49.76
0.05493841
0(Notes) Subsample of public fund injection that has multiple recipients are used. Indirect spillover
dummy takes 1 for all banks during the event days. Direct spillover dummy takes 1 for the recipient bankonly during the event days. The random effects panel data models are estimated. Reported in parentheses
are robust standard errors. *, **, or *** denotes 10%, 5%, 1% significance level, respectively. The
coefficients for the market variables and bank variables are omitted in the table.

Table 6: Delta CoVaR and TBTF: panel data IV estimation
Event idYear
Largest banks' delta CoVaR
Crisis management dummy X
Largest banks' delta CoVaR
Volatility
Change in JGB rate
Yield spread (Long)
VaR
Constant

Observations
Number of bankStd. Dev. of Individual error
Std. Dev. of Idiosyncratic error
Rho
Wald Chi (zero coeffs)
Subsample means of delta CoVaR
Largest banks, before the event
Other banks, before the event
Largest banks, after the event
Other banks, after the event
t-test
Before, Largest=other
After, Largest = other
Largest, Before=after
Other, Before =after

5
1997

8
1997

13
1998

14
1998

15
1999

40
2003

1.348***
1.199*
0.258*-0.524***1.340***
0.071***-0.46-0.656-0.147-0.201-0.136-0.017-0.378***0.742***-0.061***
0.075
1.104
0.004
-0.055-0.859-0.013-0.115-0.108-0.01526.182***-3.501-28.826***-13.463**-6.147-0.742-6.12-4.093-0.844-7.831-5.461-7.275-37.34184.798*** -33.135*** 92.332***
14.49
4.309
-35.67-10.924-9.847-24.629-27.39-10.35187.788*** -19.478*** -24.943*** -79.818*** 65.598*** 13.102**-19.12-7.396-8.96-27.254-9.71-6.359-0.608***-0.181-0.516*** -0.795***-0.037-0.914***-0.188-0.159-0.086-0.261-0.15-0.196-21.229* -45.799*** 16.907***-102.167*** 24.964***
10.328*-11.818-13.234-3.763-21.75-5.811-5.84541
2003-0.025-0.0320.013**-0.0050.839-2.3493.948-31.584
6.722-4.522-0.565**-0.234-4.291-6.112

3293
58
30.29
33.94
0.443
51.78

3237
58
24.15
31.13
0.376
281.8

3232
57
13.99
16.9
0.407
133.9

3084
57
11.89
16.49
0.342
95.77

3262
57
20.42
43.22
0.182
206.9

2938
51
10.47
13.86
0.363
42

2939
51
9.367
13.62
0.321
60.33

41.37
19.08
46.31
15.68

57.73
12.13
61.61
28.89

52.55
17.58
47.91
13.47

47.27
12.84
50.78
12.26

54.28
13.9
92.61
29.7

57.37
10.06
65.15
13.16

62.35
17.93
41.14
10.71

***
***

***
***

***
***

***
***

***
***

***
***

**

***

***

***
***
***
***

**

*

(Notes) Subsample of banks other than largest banks are used. Largest banks' delta CoVaR is endogenized by estimating it in thefirst stage (not reported). The reported second stage uses the predicted value of the largest banks' delta CoVaR. The selected eventsis related to the largest banks. Crisis management dummy takes one after each event or 0 otherwise. Reported in parentheses arerobust standard errors. *, **, or *** denotes 10%, 5%, 1% significance level, respectively.

Table 7: Average delta CoVaR: Markov regime switching model

RegimeVariables
Intercept

1

Average delta CoVaR
2

Average negative delta CoVaR
4
5
6

3

57.310(10.323)***0.110(0.128)0.057(0.138)-0.319(0.241)40.2990.000

4.113(0.623)***0.173(0.040)***0.851(0.028)***-0.134(0.032)***
6.146
0.000

0.445
(0.181)*
0.676(0.020)***0.164(0.023)***0.088(0.015)***
2.911
0.000

-1.378(0.495)**0.479(0.034)***0.440(0.034)***0.020(0.030)
5.938
0.000

Transition probability matri
1
1
0.609
2
0.109
3
0.282
4
5
6
Frequencies of the most probable state
56

2

3

4

Lag 1
Lag2
Lag3
Residual standard error
Multiple R-squared

0.012
0.529
0.459

366

-0.445-22.280(0.164)** (8.506)**
0.617
0.128
(0.042)*** (0.191)
0.142
0.027
(0.043)*** (0.420)
0.181
0.480
(0.034)*** (0.543)
2.361
17.357
0.000
0.000

5

6

0.012
0.177
0.810

1790

0.896
0.075
0.028

0.075
0.920
0.004

0.417
0.094
0.490

1086

1091

35

Table 8 : Crisis management during extremely high systemic risk: GMM panel data estimation

Fiscal Year
Number of daysall
Positive extreme state
Negative extreme state
Crisis management
positive extreme
negative extreme

ALL

1996

1997

1998

1999

2000

2001

2002

2003

2215
56
35
657
15
13

247
14
3
64
5
3

245
3
2
71
0
1

247
4
8
72
0
0

245
3
4
132
2
4

248
2
4
106
1
1

246
6
8
57
6
4

246
5
3
32
0
0

245
9
3
102
1
0

47.630***(7.120)-2.243(2.212)24.866***(5.768)26.856***(5.954)-3.035**(1.535)31.010*(17.900)-5.948***(2.038)84.569***(10.673)-5.682(9.528)-5.619***(1.822)24.498***(4.062)37.928**(15.235)
20.274***(5.921)

9.237**(4.524)53.944***(6.961)

23.124**(9.132)-0.119(1.591)12.746(9.574)9.124**(4.441)40.177***(5.872)0.322(1.518)0.005(4.056)

9.858
0.002
56.660
0.000

6.142
0.013
4.092
0.043
10.18
0.001
0.000
0.995

Sensitivities(A) Crisis management, positive extreme

34.462***(8.098)(B) Crisis management, positive normal-4.460***(0.795)(C) No crisis management, positive extrem 36.292***(9.357)(D) Crisis management, negative extreme
36.561***(8.611)(E) Crisis management, negative normal-4.701***(0.750)(F) No crisis management, negative extrem 32.771***(4.537)
Test for the equality of coefficients(A)=(C)p-value(A)=(B)p-value(D)=(F)p-value(D)=(E)
p-value

0.079
0.779
25.210
0.000
0.135
0.714
24.0300.000

82.422***(29.115)
10.075**(4.841)32.187(30.281)86.006**(41.465)
8.477(5.829)1.459(2.904)40.382***(3.988)4.996(7.228)0.968(3.139)8.848**(3.475)

5.986
0.014
6.733
0.009

3.150
0.076

0.202
0.653
0.424
0.515

-0.763(1.152)27.506***(3.883)-1.113(1.107)25.465***(4.821)26.0800.000

41.073**(20.677)
20.149***(5.680)-1.670(2.436)

2.562
0.109
4.135
0.042
1.515
0.218

0.630
0.427
6.392
0.012

(Notes) Using the inferred states by the Markov regime switching model, we identify the extreme state and normal state for average delta CoVaR and average negative delta
CoVaR, respectively. We divide each state into two for each average delta CoVaR, depending on the crisis management dummy. The base state is set to no crisis
management and normal state. Subsample of public fund injection that has multiple recipients are used. Indirect spillover dummy takes 1 for all banks during the eventdays. Direct spillover dummy takes 1 for the recipient bank only during the event days. The random effects panel data models are estimated. Reported in parentheses arerobust standard errors. *, **, or *** denotes 10%, 5%, 1% significance level, respectively. In the bottom, we report the Wald statistics for the equaliry of the coefficients foreach dummy.

3

5

12

15

22

27

37

40

0

50

Delta CoVaR
100
150

200

250

Figure 1: Cross sectional average of daily delta CoVaR

19950101

20000101
date

20050101(Note) : Delta CoVaR (%) is the standardized difference of CoVaR of financial systemi in normal
state and that of distressed state of each bank.

Figure 2: Average delta CoVaR and markov states for extreme systemic risk

Positive extreme state of systemic risk

Number of days from the beginning

Negative extreme state of systemic risk

Number of days from the beginning(Note) The grey lines in the large graph shows the exterme state for each. The small graphs show the inferredprobability of extreme state.